"So, considering all the numbers P we could guess between 0 and 100, if the truth is that something happens F out of 100 times, and doesn't happen 100 minus F out of 100 times, we want..."

This room's wall does now function as a whiteboard for people whom, like Keltham, can cast Prestidigitation.

argmax P of F*Win(P) + (100 - F)*Lose(P) = F

"...which is to say that it seems like a Lawful scoring rule must surely have this property: for every F between 0 and 100, the answer P that maximizes the sum of F of the yes-value you get from P, plus 100 minus F of the no-value you get from P, is F."

"In other words, if something happens 25 out of 100 times, then out of every possible answer between 0 and 100, 25 should do best, when it comes to adding 25 yes-values of the answer to 75 no-values of the answer."

"Putting somebody into a situation like this is what makes their answer mean, 'how often do you actually think this happens?'  There's a lot of ways to put people in weird situations where their answer could mean something else instead, because the most rewarding answer they could give isn't the one that matches reality!  Civilization tries to avoid weird situations like that, so that our words and more importantly numbers go on meaning things."

"So, considering all the numbers P we could guess between 0 and 100, if the truth is that something happens F out of 100 times, and doesn't happen 100 minus F out of 100 times, we want..."

This room's wall does now function as a whiteboard for people whom, like Keltham, can cast Prestidigitation.

argmax P of F*Yes(P) + (100 - F)*No(P) = F

"...which is to say that it seems like a Lawful scoring rule must surely have this property: for every F between 0 and 100, the answer P that maximizes the sum of F of the yes-value you get from P, plus 100 minus F of the no-value you get from P, is F."

"In other words, if something happens 25 out of 100 times, then out of every possible answer between 0 and 100, 25 should do best, when it comes to adding 25 yes-values of the answer to 75 no-values of the answer."

"Putting somebody into a situation like this is what makes their answer mean, 'how often do you actually think this happens?'  There's a lot of ways to put people in weird situations where their answer could mean something else instead, because the most rewarding answer they could give isn't the one that matches reality!  Civilization tries to avoid weird situations like that, so that our words and more importantly numbers go on meaning things."

"So, considering all the numbers P we could guess between 0 and 100, if the truth is that something happens F out of 100 times, and doesn't happen 100 minus F out of 100 times, we want..."

This room's wall does now function as a whiteboard for people whom, like Keltham, can cast Prestidigitation.

argmax P of F*Yes(P) + (100 - F)*No(P) = F

"...which is to say that it seems like a Lawful scoring rule must surely have this property: for every F between 0 and 100, the answer P that maximizes the sum of F of the yes-value you get from P, plus 100 minus F of the no-value you get from P, is F."

"In other words, if something happens 25 out of 100 times, then out of every possible answer between 0 and 100, 25 should do best, when it comes to adding 25 yes-values of the answer to 75 no-values of the answer."

"Putting somebody into a situation like this is what makes their answer mean, 'How often do you actually think this happens?'  There's a lot of ways to put people in weird situations where their answer could mean something else instead, because the most rewarding answer they could give isn't the one that matches reality!  Civilization tries to avoid weird situations like that, so that our words and more importantly numbers go on meaning things."

"So, considering all the numbers P we could guess between 0 and 100, if the truth is that something happens F out of 100 times, and doesn't happen 100 minus F out of 100 times, we want..."

This room's wall does now function as a whiteboard for people whom, like Keltham, can cast Prestidigitation.

argmax P of F*Yes(P) + (100 - F)*No(P) = F

"...which is to say that it seems like a Lawful scoring rule must surely have this property: for every F between 0 and 100, the answer P that maximizes the sum of F of the yes-value you get from P, plus 100 minus F of the no-value you get from P, is F."

"In other words, if something happens 25 out of 100 times, then out of every possible answer between '0' and '100', '25' should do best, when it comes to adding 25 yes-values of the answer to 75 no-values of the answer."

"Putting somebody into a situation like this is what makes their answer mean, 'How often do you actually think this happens?'  There's a lot of ways to put people in weird situations where their answer could mean something else instead, because the most rewarding answer they could give isn't the one that matches reality!  Civilization tries to avoid weird situations like that, so that our words and more importantly numbers go on meaning things."

"So, considering all the numbers P we could guess between 0 and 100, if the truth is that something happens F out of 100 times, and doesn't happen 100 minus F out of 100 times, we want..."

This room's wall does now function as a whiteboard for people who, like Keltham, can cast Prestidigitation.

argmax P of F*Yes(P) + (100 - F)*No(P) = F

"...which is to say that it seems like a Lawful scoring rule must surely have this property: for every F between 0 and 100, the answer P that maximizes the sum of F of the yes-value you get from P, plus 100 minus F of the no-value you get from P, is F."

"In other words, if something happens 25 out of 100 times, then out of every possible answer between '0' and '100', '25' should do best, when it comes to adding 25 yes-values of the answer to 75 no-values of the answer."

"Putting somebody into a situation like this is what makes their answer mean, 'How often do you actually think this happens?'  There's a lot of ways to put people in weird situations where their answer could mean something else instead, because the most rewarding answer they could give isn't the one that matches reality!  Civilization tries to avoid weird situations like that, so that our words and more importantly numbers go on meaning things."